Some properties and characterizations of A -normal functions

Jie Xiao

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-8

Abstract:

Let M be the set of all functions meromorphic on D = { z ∈ ℂ : | z | < 1 } . For a ∈ ( 0 , 1 ] , a function f ∈ M is called a -normal function of bounded (vanishing) type or f ∈ N a ( N 0 a ) , if sup z ∈ D ( 1 − | z | ) a f # ( z ) < ∞ ( lim | z | → 1 ( 1 − | z | ) a f # ( z ) = 0 ). In this paper we not only show the discontinuity of N a and N 0 a relative to containment as a varies, which shows ∪ 0 < a < 1 N a ⊂ U B C 0 , but also give several characterizations of N a and N 0 a which are real extensions for characterizations of N and N 0 .

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:789141

DOI: 10.1155/S0161171297000689

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